{
  "annotation_id": "e1dc3d6d-7e4c-453b-9dbb-241302d53a18",
  "date_created": "2026-02-17T05:53:08.675000Z",
  "date_modified": "2026-02-17T05:53:08.675000Z",
  "file_hash": "e3415b7fb54fdc61b68964dd790d5e5ccfe50ba182a0a4d2709ee2ae4b509a00",
  "private": false,
  "record": {
    "abstract": "We describe an explicit basis for the $\\operatorname{SU}(2)$-invariant space of the exterior power $\\wedge_{2k} \\mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum states of an electronic system with $m$ spin orbitals and $k$ electron pairs. We construct our basis by identifying the invariant space with an Artinian commutative ring called the excitation ring. We compute a Gr\\\"obner basis and enumerate its standard monomials via an explicit bijection to Dyck paths counted by the Narayana numbers.",
    "arxiv_id": "2601.06295",
    "authors": [
      "Abigail Price",
      "Ada Stelzer",
      "Svala Sverrisd\u00f3ttir"
    ],
    "categories": [
      "math.CO",
      "math.AC",
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Plane partitions and spin adapted quantum states",
    "url": "https://arxiv.org/abs/2601.06295",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "30d4fbd7-2fd8-47c5-b3a3-9495df6072cc",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}